Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C2×C42 |
| direct product | C7×#14594 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,11,10)(13,16)(14,18)(20,21,24,23)(22,26,27,25)(29,30)(33,34);(13,16)(17,19)(21,23)(22,27)(28,29,32,30)(31,34,35,33);(8,10,11,9)(12,13,15,16)(14,17,18,19)(20,22,24,27)(21,25,23,26)(28,30,32,29)(31,34,35,33);(12,14)(13,17)(15,18)(16,19)(20,23,24,21)(22,26,27,25)(28,31,32,35)(29,33,30,34)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 7582);